Writing functions f(x,y)

Question

Kaleina 2023-9-4

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评论： Alexander 2023-9-6

How do I correctly write f(x,y)=4(x-1)^2+3(y-2)^2+2(x-2)^2(y-3)^2 in MatLab code for a fiminsearch? I have been trying for days and I still cant get it right. Please help!!!

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Answer 1

Torsten 2023-9-5

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编辑：Torsten 2023-9-5

在 MATLAB Online 中打开

f = @(x,y)4*(x-1)^2+3*(y-2)^2+2*(x-2)^2*(y-3)^2;
z0 = [1 1]
z0 = 1×2
     1     1
sol = fminsearch(@(z)f(z(1),z(2)),z0)
sol = 1×2
    1.1963    2.3010
f(sol(1),sol(2))
ans = 1.0571

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Kaleina 2023-9-5

Thanks so much.

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Answer 2

Stephen23 2023-9-5

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编辑：Stephen23 2023-9-5

在 MATLAB Online 中打开

fh1 = @(x,y) 4*(x-1).^2 + 3*(y-2).^2 + 2*(x-2).^2.*(y-3).^2;
fh2 = @(v) fh1(v(1),v(2)); % function with one input
sol = fminsearch(fh2,[1,1])
sol = 1×2
    1.1963    2.3010
val = fh2(sol)
val = 1.0571

An important part of any calculation is checking the result. Lets do that now:

fsurf(fh1)

hold on

plot3(sol(1),sol(2),val,'*r')

view(54,31)

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Kaleina 2023-9-5

Thank you for the insight.

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Answer 3

Sam Chak 2023-9-5

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在 MATLAB Online 中打开

Hi @Kaleina

For a static function, especially a function of two variables, this is how I systematically find the minimum point.

% STEP 1: Find the approximate location of the minimum point via contour plot

[X, Y] = meshgrid(-1:0.1:5); % adjust these until you see the basin

Z = staticfun(X, Y); % scroll to the bottom of the script

figure(1)

contour(X, Y, Z, 30), xline(1.5, '--'), yline(2.5, '--')

xlabel('x'), ylabel('y'), colorbar

% STEP 2: Find minimum of unconstrained function f(x, y)

funhd = @(v) staticfun(v(1), v(2)); % create a function handle to pass it to fminsearch

v0 = [1.5, 2.5]; % initial guess values based on the contour plot

solution = fminsearch(funhd, v0) % applying fminsearch

solution = 1×2

1.1963 2.3010

% STEP 3a: Plot the surface and the minimum point

figure(2)

surf(X, Y, Z), hold on

minValue = funhd(solution) % insert xsol & ysol into static funtion to find the min value

minValue = 1.0571

plot3(solution(1), solution(2), minValue, 'r.', 'MarkerSize', 25) % plot the red dot

% STEP 3b: rotate for better viewing

[az, el] = view;

az = az + 180;

view(az, el)

xlabel('x'), ylabel('y'), zlabel('f(x,y)')

% Part of STEP 1: to create a function for the surface f(x, y).

function fun = staticfun(x, y)

fun = 4*(x - 1).^2 + 3*(y - 2).^2 + 2*(x - 2).^2.*(y - 3).^2;

end

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Kaleina 2023-9-5

Thats very detailed thank you.

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Answer 4

Alexander 2023-9-6

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https://ww2.mathworks.cn/matlabcentral/answers/2016776-writing-functions-f-x-y#answer_1303161

编辑：Alexander 2023-9-6

在 MATLAB Online 中打开

The solutions above are very good and should be used to avoid loops. But anyway I post my little script here, because I think it is good for the understanding how a multible dimension function is built up.

X = 0:0.1:4; % Taylor it to your needs (precision, boundary)
Y = X; % Y = -1:0.1:3;
for(ix = 1:length(X));
    for(iy = 1:length(Y))
        Z(ix,iy) = 4*(X(ix) - 1).^2 + 3*(Y(iy) - 2).^2 + 2*(X(ix) - 2).^2.*(Y(iy) - 3).^2;
    end
end
figure(1); contour(X,Y,Z);xlabel('X');ylabel('Y');
figure(2); mesh(X,Y,Z);xlabel('X');ylabel('Y');ylabel('Z');
[C, ind] = min(Z); [zMin, xInd] = min(C);
[C, ind] = min(Z'); [zMin, yInd] = min(C);
fprintf('Minimum of Z: %3.4f at pos. [X,Y] = [%i, %i], value = [%3.4f, %3.4f]\n',zMin,xInd,yInd,X(xInd),Y(yInd))